Unstable particles in matter at a finite temperature: the $\rho$ and $\omega$ mesons

Unstable particles (such as the vector mesons) have an important role to play in low mass dilepton production resulting from heavy ion collisions. Yet subtleties, such as the possibility of double counting through resonant and direct contributions, generalization of the Breit-Wigner formula for nonzero temperature and density, collisional broadening, etc., are often given insufficient emphasis. The present study attempts to point out these features using the rho and omega mesons as illustrative examples. Effects of non-zero temperature and density through vector meson masses and decay widths on dilepton spectra are studied within the framework of Walecka-type model